I'm having an issue with a particular question in that the limits are not being used (only the upper limit is being used). If I use only the upper limit, I get the correct answer, but if I use both limits, the area comes in -ve and becomes wrong.

I would just like to know why.

The equation of the following curve is: x^3-3x^2-9x+27.

The integrated equation becomes: x^4/4 - x^3 -9x^2/2 +27x.

Here's the figure:

Using x=3 gives us 33.75 as the area. This is the answer.

But what about x=0? If I use this and subtract the results, I get -47.25.

Any explanation would be helpful.